Hi Wei En,
My case (3 doses of vaccine) may not apply to you. My COVID-19 digital certificate recognized by EU had been verified while I checked in at a airline counter in Taiwan. My final Italy destination is Torino and had connecting flight in Amsterdam. Nobody asked me to show them with my COVID-19 digital certificate at both airports. For my understanding, 2 doses of vaccine is required to entering EU and Italy. So, avoiding any problems and suggesting you to have 2nd Pfizer vaccine before entering Italy.